Application of Honey Bee Mating Optimization on Distribution State Estimation Including Distributed...

Application of Honey Bee Mating Optimization on Distribution State Estimation Including Distributed

Generators

Jia-Xian Zhu

Introduction

• Distribution State Estimation (DSE)

• Distributed Generators (DGs)

• Load

• Static Var Compensators (SVCs)

• Voltage Regulators (VRs)

• Under Load Tap Changer (ULTC)

Introduction

• Online monitoring of power distribution systems plays a key role in this part of power systems and improve efficiency and reliability of the power distribution system.

• The performance of online monitoring highly depends on the quality of load data and DG outputs.

Introduction

• A number of DSE methods have been developed in distribution systems, which are divided into two main categories.– Statistical methods, which usually use an iterative convergence

method.– Load adjustment state estimation, which usually utilize sensitivity

analysis.

• It is assumed that the objective functions and constraints should be continuous and differentiable.

• Due to the existence of distributed generation, as well as SVC and transformer tap changers with discrete performance.

Introduction

• Recently, a new optimization algorithm based on honey bee mating has been used to solve difficult optimization problems such as optimal reservoir operation and clustering.

• In this paper, a new approach based on HBMO for a practical distribution state estimation including DGs, SVC and VRs is presented.

• The proposed approach is compared with the methods based on neural networks, Ant Colony Optimization (ACO), and genetic algorithms for two test systems.

Distribution State Estimation Including Distributed Generators

The state variables vector including the loads’ and DGs’ outputs.

zi The ith measured values.

wi The weighting factor of the ith measured variable.

hi The state equation of the ith measured variable.

m the number of measurements.

Ng The number of DGs with variable outputs.

NL The number of loads with variable outputs.

PiG The active power of the ith DG.

Piload The active power of the ith load.

X


The absolute power flowing over distribution lines.

The maximum transmission power between the nodes i and j.

Tapi The current tap positions of the ith transformer.

Nt The number of transformers and VRs installed along feeder.

Vi the actual voltage magnitude of the ith bus.

Qic The reactive power of the ith capacitor.

Nc The number of capacitors installed along feeder.

LineijP

LineijP max,


• In order to have a unique solution, these assumptions should be made:– Status of distribution lines and switches is known.– A contracted load and distributed generation values ar

e known at each node.– Voltage and current at the substation bus (main bus)

are known.– If outputs of DGs and loads are fixed, the outputs and

power factors will be available.– If outputs of DGs and loads are variable, the average

outputs, the standard deviations and the power factors can be obtained.

– Set points of VRs and local capacitors are known.


• Objective function

]LN

LoadP,...,2

LoadP,1

Load[PLP

]NgGP,...,2

GP,1G[PGP

]LoadP,GP[X

2))X(ih i(zm

1i iω )Xf( Min


• Constraints– Active power constraints of DGs:

– Distribution line limits:

– Tap of transformers:

g1,2,3,...Ni imaxG,

PiG

PiminG,

P

Linemax,ij

Lineij PP

tiii NiTapTapTap ...,,2,1maxmin


• Constraints– Bus voltage magnitude:

– Active power constraints of loads:

– Reactive power constraint of capacitors:

maximin VVV

L1,2,3,...Ni iLoad.max

PiLoad

PiminLoad,

P

cN1,2,3,...,i imaxc,

Qic

Q0

Honey-bee modeling

• A colony may contain one queen or more during its life-cycle, which are named monogynous and/or polygynous colonies.

• Broods arise either from fertilized or unfertilized eggs.– The former represent potential queens or workers, whereas the l

atter represent prospective drones.• A queen is the only member of a colony capable of layin

g eggs which are fertilized by spermatozoa.– A queen life time is 6-7 years.

• Drones' sole function is to mate with the queen.– They live about eight weeks.– Any drones left at the end of the season are considered non-ess

ential and will be driven out of the hive to die.

Honey-bee modeling

• Worker bees do all the different tasks needed to maintain and operate the hive.– Workers born early in the season will live abo

ut 6 weeks while those born in the fall will live until the following spring.

• Mating flight.• Only the queen bee is fed ‘‘royal jelly”. ‘‘Nu

rse bees’’ secrete this nourishing food from their glands and feed it to their queen.

Honey-bee modeling

List of Drones

Select a Drone

at Random

Queen

Selected Drone

Mate

Brood Apply

Local

Search

Brood

Selected Best

Selected

Brood

Replace the queen if

the best brood is better

than the queen

Application of the HBMO to Distribution State Estimation

• Step 1: Define the input data– The speed of queen at the start of a mating fligh

t (Smax).– The speed of queen at the end of a mating flight

(Smin).– The speed reduction schema (), the number of

iteration, the number of workers (NWorker).– The number of drones (NDreone).– The size of the queen's spermatheca (NSperm ).– The number of broods (NBrood).


• Step 2: Transfer the constraint DSE to the unconstraint DSE– f(X) is the objective function values of DSE problem.

– Neq and Nueq are the number of equality and inequality constraints, respectively.

– hi(Xi) and gi(Xi) are the equality and inequality constraints.

– K1 and k2 are the penalty factors, respectively.

Nueq

jij

N

jij XgMaxkXhkXfXF

eq

1

22

1

21 )])(,0[(())((()()(


• Step 3: Generate the initial population

Lg

Lj

maxLoad,j

iLoad,j

minLoad,

gjmaxG,

jiG,

jminG,

NiLoad,

2iLoad,

1iLoad,

NiG,

2iG,

1iG,n1ji

N

2

1

NNn

N,1,2,3,....j PPP

N,1,2,3,....j PPP

..n1,2,3,....i] P,...,P,P,P,....,P,[P]xX

X

X

X

Population

Lg

[


• Step 4: Calculate the augmented objective function value

• Step 5: Sort the initial population based on the objective function values

• Step 6: Select the queen


• Step 7: Generate the queen speed– The queen speed is randomly generated as:

• Step 8: Select the population of drones– The population of drones is selected from the sorted

initial population as:

DroneN

iLoad,2

iLoad,1

iLoad,NiG,

2iG,

1iG,i

N

N,1,2,3,....i ],P,...,P,P,P,....,P,[PD

D

D

D

PopulationDrone

Lg

Drone

2

1

_

minminmax )((.) SSSrandSqueen


• Step 9: Generate the queen's spermatheca matrix (Mating flight) – At the start of the mating flight, the queen flies with her maximum

speed.– A drone is randomly selected from the population of drones.– The mating probability is calculated based on the objective functi

on values of the queen and the selected drone.

• Prob(D) is the probability of adding the sperm of drone D to the spermatheca of the queen, (f) is the absolute difference between the fitness of D and the fitness of the queen and S(t) is the speed of the queen at time t.

• The probability of mating is high when the queen is with the high speed level, or when the fitness of the drone is as good as the queen's.

))t(S/)f(exp()D(obPr


– A number between 0 and 1 is randomly generated and compare

d with the calculated probability. • If it is less than the calculated probability, the drone's sperm is sorte

d in the queen's spermatheca and the queen speed is decreased.

• Otherwise, the queen speed is decreased and another drone from the population of drones is selected until the speed of the queen reaches to her minimum speed or the queen's spermatheca is full.

)t(S)t(S 1

SpermN

iLoad,2

iLoad,1

iLoad,NiG,

2iG,

1iG,n1ji

N

N,1,2,3,....i ],P,...,P,P,P,....,P,[P]s[Sp

Sp

Sp

Sp

matrix_caSpermacthe

Lg

Sperm

2

1


• Step 10: Breeding process

– Where β is a random number between 0 and 1. Broodj is the jth brood.

Brood

nbi

nbest

nbest

mbi

mbest

mbest

mbestbestbestj

nbi

mbiiii

nbest

mbestbestbestbest

N,...,,j

,)sx(x....)sx(xx....xxBrood

s........s....ssSp

x........x....xxX

321

11121

21

21


• Step 11: Feeding selected broods and queen with the royal jelly by workers– Improve the newly generated set of solutions employing different

heuristic functions and mutation operators according to their fitness values.

• Step 12: Calculate the augmented objective function value for the new generated solutions– The augmented objective function is to be evaluated for each

individual of the new generated solutions by using the result of distribution load flow. If the new best solution is better than the queen replace it with queen.

• Step 13: Check the termination criteria– If the termination criteria satisfied finish the algorithm, else

discard all previous trial solutions and go to step 3 until convergence criteria met.

Simulation results

• It is assumed that the following information is available.– Value of output for constant loads and DGs.– Average value and standard deviation for vari

able DGs and loads.– Values of measured points– Power factor of Loads and DGs– Set points of VRs and local capacitors

Simulation results

• For this system it is assumed that there are three DGs connected at buses 6, 17 and 29.

Simulation results

• Comparison of measured and estimated values for DGs

DG No

HBMO ACO GA NN

actual estimated actual estimated actual estimated actual estimated

G1 56 57.1 56 56.3 56 57.36 56 58.2

G2 85 84.2 85 86.9 85 83.43 85 84.2

G3 85 85.6 85 86.3 85 87.67 85 87.64

Simulation results

• Comparison of execution time

• Comparison of average and standard deviation for different executions

Method HBMO ACO GA NN

Execution time(s) 15-20 20-40 100-120 ~0

Method Average Standard Deviation (%)

ACO 0.0002 10

GA 0.0003 12

NN 0.0012 0

HBMO 0.00018 8

Simulation results

• Maximum Individual Relative Error

• Maximum Individual Absolute Error

• where Xest and Xtrue are the estimated and actual values, respectively.

100 ))i(X/)i(X)i(Xmax((%)MIRE truetrueest

))()(max((%) iXiXMIAE trueest

Simulation results

• Comparison of errors for estimated loadsACO HBMO NN GA

MIRE(%) value 4.8823 4.095 5.13 5.33

location 30 29 2 2

MIAE(%) value 1.67 1.24 4.31 1.77

location 29 12 12 30

Simulation results

• Comparison of errors for estimated DGsACO HBMO NN GA

MIRE(%) value 2.235 1.96 3.93 3.141

location DG2 DG1 DG1 DG3

MIAE(%) value 1.9 1.1 2.64 2.67

location DG2 DG1 DG3 DG3

Simulation results

• A single line diagram of 80-bus test system

Substation

VR3

VR1

VR2

VR4

C1

C2

C3

C4

C5

Simulation results

• Comparison of execution time

• Comparison of average and standard deviation for different executions

Method HBMO ACO GA NN

Execution time(s) 15-20 30-40 120-130 ~0

Method Average Standard Deviation (%)

ACO 0.0004 10

GA 0.0009 13

NN 0.0018 0

HBMO 0.00019 8

Application of Honey Bee Mating Optimization on Distribution State Estimation Including Distributed...

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